How many solutions does the following system have over the interval (-3, 1]?

f(x)= In(x+3)

g(x)= 2*6^x

Answer:

45

Step-by-step explanation:

50-5=45

Based on the information provided, we cannot conclude with certainty that the average pickup order has a higher amount than the average delivery order.

Based on the information given, we can conclude that there is a 95% chance that the true mean for pickup orders falls between $33 and $51, and the true mean for delivery orders falls between $21 and $41. However, we cannot conclude with certainty that the average pickup order has a higher amount than the average delivery order.

To determine if there is a significant difference between the means of the two groups, we need to perform a hypothesis test. We can set up our null hypothesis as "there is no significant difference between the means of the pickup and delivery orders" and our alternative hypothesis as "the average pickup order has a higher amount than the average delivery order."

We can use a two-sample t-test to test this hypothesis. Assuming equal variances, we would calculate the test statistic as

t = (xpickup - xdelivery) / (s / √n)

where xpickup and xdelivery are the sample means for pickup and delivery orders, s is the pooled standard deviation, and n is the sample size for each group.

If our calculated t-value is greater than the critical value at a chosen significance level (e.g. 0.05), we can reject the null hypothesis and conclude that there is a significant difference between the means of the two groups.

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A dilation of a line is a transformation that changes the size of the line but preserves its shape.

It is a type of similarity transformation. A dilation can either be a reduction, in which the line is made smaller, or an enlargement, in which the line is made larger. In both cases, the line's shape is preserved, but the size is changed.

The center of dilation, also known as the scale factor, is a fixed point around which a dilation takes place. The scale factor is a value that represents the amount of change in size, it can be greater than 1 for an enlargement or less than 1 for a reduction.

In geometry, a dilation is represented by a multiplication of the coordinates of a point by a scale factor. For example, a dilation of a line with a scale factor of 2 will result in the line being twice as long as the original line.

In conclusion, a dilation of a line is a transformation that changes the size of the line but preserves its shape. The center of dilation or scale factor is a fixed point around which a dilation takes place and is represented by a multiplication of the coordinates of a point by a scale factor.

It can be either an enlargement or a reduction depending on the scale factor value.

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The area of a shape is the amount of space on it:

The shaded area is 314 square centimeters

Start by calculating the area of sectors OFG and OAD using:

\(A = \frac{\theta}{360} * \pi r^2\)

So, we have:

\(OFG = \frac{40}{360} * \pi * 18^2\)

\(OFG = 36\pi\)

Also, we have:

\(OAD = \frac{40}{360} * \pi * 18^2\)

\(OAD = 36\pi\)

Next, calculate the area of the sectors BOE and COH

Note that the radius of these sectors is 6 cm.

So, we have:

\(COH =BOE = \frac{140}{360} * \pi * 6^2\)

\(COH = BOE = 14\pi\)

The shaded area is then calculated as:

\(Shaded = OFG + OAD + COH + BOE\)

This gives

\(Shaded =36\pi + 36\pi + 14\pi + 14\pi\)

\(Shaded =100\pi\)

The equation becomes

\(Shaded =100 * 3.14\)

\(Shaded = 314\)

Hence, the shaded area is 314 square centimeters

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Answer:

6/12

Step-by-step explanation:

Got it right on test

Answer: 6 / 12

Step-by-step explanation: I took the test 2 hours ago xD

Answer:

8 is 7 less than 15

The domain is the set of all the x-values used by those points.

  { -1, 0, 3, -5, -3 }

The order does not matter.

The Equation of circle is (x-2)² +(y+ 8)² = 7²

The standard form of a circle with center (h, k) and radius r is given by the equation:

(x-h)²  + (y-k)² = r²

In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

In this case, the center of the circle is (2, -8) and the radius is 7.

Plugging these values into the equation, we have:

(x- 2)² + (y- (-8))² = 7²

Simplifying further:

(x-2)² +(y+ 8)² = 7²

So, the equation in standard form for the circle with center (2, -8) and radius 7 is:

(x-2)² +(y+ 8)² = 7²

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The equation of the tangent plane is:
2x - 6y - z + 15 = 0

To find the equation of the tangent plane to the surface z = xy - x - y at the given point (-5, 3, -13), we first need to find the partial derivatives with respect to x and y, which will give us the normal vector to the plane.

∂z/∂x = y - 1
∂z/∂y = x - 1

Now, we can plug in the given point (-5, 3, -13) to find the normal vector components:

∂z/∂x(-5, 3) = 3 - 1 = 2
∂z/∂y(-5, 3) = -5 - 1 = -6

Thus, the normal vector to the plane is <2, -6, -1>.

Now we can use the point-normal form of the plane equation:

A(x - x₀) + B(y - y₀) + C(z - z₀) = 0

Plugging in the normal vector components and the given point, we get:

2(x - (-5)) - 6(y - 3) - 1(z - (-13)) = 0

Simplify the equation:

2x + 10 - 6y + 18 - z - 13 = 0
2x - 6y - z + 15 = 0

So the equation of the tangent plane is:

2x - 6y - z + 15 = 0

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Answer:

1/1000

Step-by-step explanation:

The density is 1.7 x 10^-27 kg/m^3.

The density of a proton can be determined by calculating its mass and volume. Given the volume of a sphere, the density of a proton can be expressed to two significant figures.

To determine the density of a proton, we need to calculate its mass and volume. The mass of a proton is approximately 1.67 x 10^-27 kilograms. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius. Since a proton is considered a point particle, it does not have a defined radius. Therefore, we assume the radius to be extremely small, close to zero. Substituting this value into the volume equation, we get V = (4/3)π(0)^3 = 0. However, the mass of the proton remains unchanged. Thus, the density of a proton is approximately 1.67 x 10^-27 kilograms per cubic meter. Rounded to two significant figures, the density is 1.7 x 10^-27 kg/m^3.

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Answer:

48

Step-by-step explanation:

the top shape is 6 by 6, which is 36

the bottom shape is 3 by 4, which is 12.

if you add the two areas, 12+36, you get 48. so the area of the entire shape is 48mi

Answer:

There were 206 more people on Thursday than on Monday.

Step-by-step explanation:

520 - 314 = 206

So, the probability of ending up with a three-digit number that is divisible by 4 is 1/24.

To find the probability of ending up with a three-digit number that is divisible by 4 when spinning the spinner three times, we need to consider the possible outcomes that satisfy this condition and divide it by the total number of possible outcomes. Let's analyze the given spinner and its possible outcomes:

Spinner: [1, 2, 3, 4, 5, 6]

To form a three-digit number, the hundreds digit will be determined by the first spin, the tens digit by the second spin, and the units digit by the third spin. A number is divisible by 4 if the last two digits (tens and units digits together) form a number divisible by 4. Therefore, we need to find the number of possible outcomes for the tens and units digits that satisfy this condition.

Possible outcomes for the tens digit: [2, 4, 6]

Possible outcomes for the units digit: [2, 4, 6]

Combining the possible outcomes for the tens and units digits, we have a total of 9 (3 possibilities for the tens digit multiplied by 3 possibilities for the units digit) favorable outcomes. The total number of possible outcomes for each spin is 6 (since there are 6 numbers on the spinner). Since we are spinning the spinner three times independently, the total number of possible outcomes for spinning it three times is 6^3 = 216. Therefore, the probability of ending up with a three-digit number divisible by 4 is:

Probability = favorable outcomes / total outcomes

Probability = 9 / 216

Probability = 1 / 24

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The probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1

Note that the ratios =  5:4:2:3

toffee: coffee: orange: mint chocolates = 5:4:2:3:1

Total ratio = 15

Probability of picking a hazelnut chocolate = ratio of hazelnut chocolates/ total ratio

Probability of picking a hazelnut chocolate  = \(\frac{1}{15}\)

The number of hazelnut chocolates in the box is gotten from the ratio which is 1

Therefore, the probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1

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Answer: 0.39

Step-by-step explanation:

We are required to determine the the value of f, rounded to the nearest hundredth

The value of f, rounded to the nearest hundredth is 0.39

Given function:

\(d(v) = \frac{2.15 {v}^{2} }{64.4f} \)

Where,

d = stopping distance in feet

v = initial velocity in miles per hour

f = a constant related to friction

When

v = 40 mph

d = 138 ft

f = ?

\(d(v) = \frac{2.15 {v}^{2} }{64.4f} \)

\(138= \frac{2.15 {(40)}^{2} }{64.4f} \)

138(64.4f) = 2.15(1600)

8,887.2f = 3440

f = 3440 / 8,887.2

f = 0.3870735439733

Approximately to the nearest hundredth f = 0.39

Therefore, the value of f, rounded to the nearest hundredth is 0.39

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Answer: y = 2x - 11

Step-by-step explanation:

A linear equation has the following form.

y = a . x + b

where,

y: independent variable

a: slope

x: independent variable

b: y-intercept

The slope is 2, so a is 2. The ordered pair (4, -3) means that when x takes the value 4, y takes the value -3. We can replace these values in the general equation to find the y-intercept.

y = a . x + b

-3 = 2 . 4 + b

b = -11

The linear equation is

y = 2x - 11

Answer:

C. is the correct option

Step-by-step explanation:

When we find the equation using the point and slope formula, we get y=-3x+10

As you can see, that doesn't match any of the answers, since it is in the point-slope formula.

We can start solving all the equations to rule out the correct one, but to save yourself from reading all of this, I'll just do there C.

For this equation, we will distribute the 3, and then add 4 to both sides.

y-4=-3(x-2) --->  y-4=-3x+6 ---> y-4(+4)=-3x+6(+4) ---> y=-3x+10

This leads back to the original equation so we know it is correct.

To prove the theorem by contradiction, we start by assuming the fact that there exist two real numbers, x, and y, such that (x+y)/2 is greater than both x and y individually, i.e., (x+y)/2 > x or (x+y)/2 > y. So, the first option is correct.

The proof by contradiction of the theorem starts by assuming that: "There exists two real numbers, x, and y, such that (x+y)/2 > x and (x+y)/2 > y." The proof by contradiction of the theorem is as follows:

Suppose, for the sake of contradiction, that (x+y)/2 > x and (x+y)/2 > y for all real numbers x and y.

This implies that (x+y) > 2x and (x+y) > 2y.

Adding these inequalities gives 2x + 2y < 2(x + y), or equivalently, x + y < x + y, which is impossible, since x + y = x + y for all real numbers x and y. Therefore, our initial assumption that (x+y)/2 > x and (x+y)/2 > y for all real numbers x and y must be false.

So there must be at least one pair of real numbers x and y such that (x+y)/2 ≤ x or (x+y)/2 ≤ y, which proves the theorem.

Hence, the option that is correct is - "There exists two real numbers, x, and y, such that (x+y)/2 > x or (x+y)/2 > y."

"There exists two real numbers, x, and y, such that (x+y)/2 > x or (x+y)/2 > y." This assumption is made to establish the contradiction that leads to the proof of the theorem.

The concept being used in the proof by contradiction is the assumption that contradicts the theorem in order to demonstrate that the theorem must be true.

In this case, the theorem states that the average of any two real numbers is less than or equal to at least one of the two numbers. The proof by contradiction aims to show that this statement is always true by assuming the opposite and reaching a contradiction.

The assumption made is that there exist two real numbers, x, and y, such that (x+y)/2 > x or (x+y)/2 > y. This assumption implies that the average of x and y is greater than one or both of the numbers individually.

To prove the theorem by contradiction, the assumption is examined and shown to lead to a contradiction with the properties of real numbers. This contradiction arises when it is shown that the assumption cannot hold true for all possible choices of x and y.

By reaching a contradiction, it demonstrates that the initial assumption was false, and therefore the opposite must be true. Hence, the theorem is proven to be valid: the average of any two real numbers is indeed less than or equal to at least one of the two numbers.

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Answer:

24.075, 24.008, 21.605, 21.048

If the price of one ticket of bus is $180 and the bus has 56 seats then the maximum revenue that it can earn is $5107.6

Given that the price of a bus ticket to Saskatoon is $180 and the bus has 56 seats.

We are required to find the maximum revenue that the bus company can earn.

Suppose x represents the number of seats, y represents the total amount.

Price=$156

Seats=56

When the bus is of half capacity the bus seats will be 28.

As price decreases th rider gains 2 more.

Revenue equation.

y=(156.5x)(28+2x)-------------1

Expanding the equation.

y=4368-140x+312-10\(x^{2}\)

Differentiating with respect to x.

dy/dx=0-140+312-20x

=172-20x

Put dy/dx=0

172-20x=0

x=8.6

Substitute the value of variable x in the equation 1.

y=(156-5x)(28+2x)

=$5107.6

Hence the maximum revenue that the bus company can earn is $5107.6.

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The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.

The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.

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Answer:

Step-by-step explanation:

I think the best way is to split up the erasers before you do anything. That would mean there were 20 gift bags in all

If you did that, then each gift bag would contain 2 pencils with 10 left over.

Further 130 pens would divide up into 6 pens in each gift bag with 10 pens left over.

Answer:

(1)

Step-by-step explanation:

This is because (x-7)²=(x-7)(x-7), which when expanded using the FOIL method, is equal to x²-7x-7x+49=x²-14x+49.

Answer:

y = -1/3x - 1

Step-by-step explanation:

Let's solve for y.

Step 1: Add -x to both sides.

x+3y+−x=−3+−x

3y=−x−3

Step 2: Divide both sides by 3.

y=-1/3x-1

--

\(\frac{-1}{3} x-1\)